Suppose I have m observations from a time series before some specified date, and n additional observations after that date. The mean of the time series is expected to change on that date by an unknown amount, without further changes to the time series. Given the m + n observations and the date of the expected change, how does one test for a change in mean?
As an example, think about new traffic rules, that are expected to decrease the number of accidents in some country. We have the daily number of accidents in the country for, say, the 60 days before the new rules change, and for 40 days after the rules change, and want to know if the change did any good, i.e., lowered the number of accidents. Importantly, the observations may not be assumed to be independent, so a simple two-sample t test or Wilcoxon test aren't appropriate; any reasonable correlation structure - say, AR(1) - may be assumed. In my specific application, both m and n are around 10.
Any help will be greatly appreciated.